Higher June 2025 Paper 1 Q20
20. The sketch below shows a circle with diameter PQ.
The line \(y - 2x + 5 = 0\) is a tangent to the circle at the point Q.
Find the equation of the line PQ.
Write your answer in the form \(ax + by + c = 0\). [5]
Diagram not drawn to scale
| Scheme | Marks | Comments |
|---|---|---|
| Gradient of \(PQ = -1/2\) | B2 | B1 for gradient of tangent = 2 Correct use of \(-\frac12\) implies B2 e.g. \(y + \frac12x \ldots = 0\) or \(y = -\frac12x \ldots\) |
| \(y - 4 = -\frac12(x - 3)\) or \(4 = -\frac12\times3 + c\) oe | M1 | |
| \(2y - 8 = -x + 3\) or \(y = -\frac12x + 5{\cdot}5\) oe | A1 | |
| \(x + 2y - 11 = 0\) or \(\frac12x + y - 5.5 = 0\) | A1 | FT from one slip provided M1 awarded Mark final answer |
| (5) |